It is better than that: Netscape was actually the browser ignoring standards (and in particular was refusing to implement CSS) and Microsoft with IE came in as what someone from the W3C at the time called the "white knight" with a browser that cared about standards and published their DTDs and really implemented stuff like CSS. They (of course) ran into the typical-MS problem of "we implemented a draft and then they made a major change (to the box model, which ironically later got a configuration flag for and many many people actively prefer the old MS way ;P) and couldn't update very well as we now had existing users", but what I claim really caused them to stagnate was the massive lawsuit against them, which demoralized the IE team in a company that doesn't force people to work on project teams where they don't want to work (the culture in Microsoft was "if you want to build a new product, poach a team worth of people from other, more boring teams").
For more information and a million references, here is a comment I left detailing this history five years ago: